Finite-dimensional superalgebra realization conjecture for identities with superinvolution

Let $F$ be a field of characteristic zero, and let $A=A_{\bar{0}} \oplus A_{\bar{1}}$ be a finitely generated associative PI-superalgebra over $F$ with superinvolution.

Finite-dimensional realization conjecture. There exists a finite-dimensional associative superalgebra $C=C_{\bar{0}} \oplus C_{\bar{1}}$ over $F$ with superinvolution that satisfies the same identities with superinvolution as $A$.

This conjecture proposes a finite-dimensional representative for the identities of every finitely generated associative PI-superalgebra with superinvolution. It is motivated by analogous results for ordinary algebras with involution, but the source gives no resolution of the superinvolution version.